Question

Find the square root of the following numbers:
(i) $1444$ (ii) $1849$ (iii) $5776$ (iv) $7921$

Answer 1

(i)

$\begin{array}{cc}1444& =2\times 2\times 19\times 19\\ \sqrt{1444}& =\sqrt{2\times 2\times 19\times 19}\\ & =2\times 19\\ & =38\end{array}$

(ii)

$\begin{array}{cc}1849& =43\times 43\\ \sqrt{1849}& =\sqrt{43\times 43}\\ & =43\end{array}$

(iii)

$\begin{array}{cc}5776& =2\times 2\times 2\times 2\times 19\times 19\\ \sqrt{5776}& =\sqrt{2\times 2\times 2\times 2\times 19\times 19}\\ & =2\times 2\times 19\\ & =76\end{array}$

(iv)

$\begin{array}{cc}7921& =89\times 89\\ \sqrt{7921}& =\sqrt{89\times 89}\\ & =89\end{array}$